Several recent proposals for sharing congestion information across concurrent flows between end-systems overlook an important problem: two or more flows sharing congestion state may in fact not share the same bottleneck. In this paper, we categorize the origins of this false sharing into two distinct cases: (i) networks with QoS enhancements such as differentiated services, where a flow classifier segregates flows into different queues, and (ii) networks with path diversity where different flows to the same destination address are routed differently. We evaluate the impact of false sharing on flow performance and investigate how false sharing can be detected by a sender. We discuss how a sender must respond upon detecting false sharing. Our results show that persistent overload can be avoided with window-based congestion control even for extreme false sharing, but higher bandwidth flows run at a slower rate. We find that delay and reordering statistics can be used to develop robust detectors of false sharing and are superior to those based on loss patterns. We also find that it is markedly easier to detect and react to false sharing than it is to start by isolating flows and merge their congestion state afterward.